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The average of 10 numbers is 17. The first number is increased by 1, the second by 2 and so on such that the tenth number is increased by 10. What is the new average?
  • a)
    22.5
  • b)
    23.5
  • c)
    22
  • d)
    Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The average of 10 numbers is 17. The first number is increased by 1, t...
The sum of the numbers will increase by 1 + 2 + 3 + 4 + . . . + 10 = 55
Thus, the average will increase by 55/10 = 5.5
Thus, the new average is 17 + 5.5 = 22.5
Hence, option 1.
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Most Upvoted Answer
The average of 10 numbers is 17. The first number is increased by 1, t...
Given:
- The average of 10 numbers is 17.
- The first number is increased by 1, the second by 2, and so on such that the tenth number is increased by 10.

To find:
- The new average of the 10 numbers after the increase.

Solution:
Let's assume the sum of the original 10 numbers is S.

The average of the original 10 numbers is given as 17. So, we have:
S/10 = 17

Now, let's calculate the sum of the new numbers after the increase.

The first number is increased by 1, so the new first number is (original first number + 1).
Similarly, the second number is increased by 2, so the new second number is (original second number + 2).
And so on, the tenth number is increased by 10, so the new tenth number is (original tenth number + 10).

The sum of the new numbers after the increase is given as:
(S + 1 + 2 + 3 + ... + 10)

The sum of the first 10 natural numbers can be calculated using the formula:
Sum = (n * (n + 1))/2

Using this formula, the sum of the new numbers after the increase is:
(S + (1 + 2 + 3 + ... + 10))
= (S + (10 * 11)/2)
= (S + 55)

Now, the number of terms in the new series is still 10, so the new average can be calculated as:
(S + 55)/10

Since we need to find the new average, we substitute the value of S from the given equation:
17 * 10 = S
S = 170

Substituting the value of S in the new average equation:
New Average = (170 + 55)/10
= 225/10
= 22.5

Hence, the new average of the 10 numbers after the increase is 22.5.

Therefore, the correct answer is option A) 22.5.
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The average of 10 numbers is 17. The first number is increased by 1, the second by 2 and so on such that the tenth number is increased by 10. What is the new average?a)22.5b)23.5c)22d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
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